1. Field
This invention relates generally to the modulation of communications and, more particularly, to systems and methods for generating a quadrature modulation rotating training signal for use in the training of receiver channel estimates.
2. Background
FIG. 1 is a schematic block diagram of a conventional receiver front end (prior art). A conventional wireless communications receiver includes an antenna that converts a radiated signal into a conducted signal. After some initial filtering, the conducted signal is amplified. Given a sufficient power level, the carrier frequency of the signal may be converted by mixing the signal (down-converting) with a local oscillator signal. Since the received signal is quadrature modulated, the signal is demodulated through separate I and Q paths before being combined. After frequency conversion, the analog signal may be converted to a digital signal, using an analog-to-digital converter (ADC), for baseband processing. The processing may include a fast Fourier transform (FFT).
There are a number of errors that can be introduced into the receiver that detrimentally affect channel estimations and the recovery of the intended signal. Errors can be introduced from the mixers, filters, and passive components, such as capacitors. The errors are exacerbated if they cause imbalance between the I and Q paths. In an effort to estimate the channel and, thus, zero-out some of these errors, communication systems may use a message format that includes a training sequence, which may be a repeated or predetermined data symbol. Using an Orthogonal Frequency Division Multiplexing (OFDM) system for example, the same IQ constellation point may be transmitted repeatedly for each subcarrier.
In an effort to save power in portable battery-operated devices, some OFDM systems use only a single modulation symbol for training. For example, a unique direction in the constellation (e.g., the I path) is stimulated, while the other direction (e.g., the Q path) is not. The same type of unidirectional training may also be used with pilot tones. Note: scrambling a single modulation channel with ±1 does not rotate the constellation point, and provides no stimulation for the quadrature channel.
In the presence of quadrature path imbalance, which is prevalent in large bandwidth systems, the above-mentioned power-saving training sequence results in a biased channel estimate. A biased channel estimate may align the IQ constellation well in one direction (i.e., the I path), but provide quadrature imbalance in the orthogonal direction. It is preferable that any imbalance be equally distributed among the two channels.
FIG. 2 is a schematic diagram illustrating quadrature imbalance at the receiver side (prior art). Although not shown, transmitter side imbalance is analogous. Suppose that the Q path is the reference. The impinging waveform is cos(wt+θ), where θ is the phase of the channel. The Q path is down-converted with −sin(wt). The I path is down-converted with (1+2ε)cos(wt+2Δφ). 2Δφ and 2ε are hardware imbalances, respectively a phase error and an amplitude error. The low pass filters HI and HQ are different for each path. The filters introduce additional amplitude and phase distortion. However, these additional distortions are lumped inside 2Δφ and 2ε. Note: these two filters are real and affect both +w and −w in an identical manner.
Assuming the errors are small:(1+2ε)cos(wt+2Δφ)≈(1+2ε)cos(wt)−2Δφ.sin(wt)
The first component on the right hand side, cos(wt), is the ideal I path slightly scaled. The second component, −2Δφ.sin(wt), is a small leakage from the Q path. After down-conversion of the impinging waveform:                in the I path: (1+2ε)cos(θ)+2ε.sin(θ).        in the Q path: sin(θ).        
The errors result in the misinterpretation of symbol positions in the quadrature modulation constellation, which in turn, results in incorrectly demodulated data.